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Grade 11 Math Lab: Transcendence & Limits FREE
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Polynomial Functions
Learning Objectives
- Analyze polynomial behavior
- Find roots and multiplicity
- Sketch graphs
Key Concepts
Degree
Highest exponent determines end behavior
Multiplicity
How many times a root appears
Theory
**End Behavior:**
- Even degree: Same direction both ends
- Odd degree: Opposite directions
- Positive leading: Right side up
- Negative leading: Right side down
**Multiplicity Effects:**
- Odd: Graph crosses x-axis
- Even: Graph touches and bounces
Examples
Describe f(x) = -x³ + 2x
Solution: Odd degree, negative lead → rises left, falls right